Classifying Causal Structures: Ascertaining when Classical Correlations are Constrained by Inequalities

• URL: http://arxiv.org/abs/2308.02380v1
• Date: Fri, 4 Aug 2023 15:23:55 GMT
• Title: Classifying Causal Structures: Ascertaining when Classical Correlations are Constrained by Inequalities
• Authors: Shashaank Khanna, Marina Maciel Ansanelli, Matthew F. Pusey, and Elie Wolfe
• Abstract summary: We develop methods for detecting causal scenarios that impose inequality constraints versus those which do not. Many scenarios with exclusively equality constraints can be detected via a condition articulated by Henson, Lal and Pusey. We are able to resolve all but three causal scenarios, providing evidence that the HLP condition is, in fact, exhaustive.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The classical causal relations between a set of variables, some observed and some latent, can induce both equality constraints (typically conditional independences) as well as inequality constraints (Instrumental and Bell inequalities being prototypical examples) on their compatible distribution over the observed variables. Enumerating a causal structure's implied inequality constraints is generally far more difficult than enumerating its equalities. Furthermore, only inequality constraints ever admit violation by quantum correlations. For both those reasons, it is important to classify causal scenarios into those which impose inequality constraints versus those which do not. Here we develop methods for detecting such scenarios by appealing to d-separation, e-separation, and incompatible supports. Many (perhaps all?) scenarios with exclusively equality constraints can be detected via a condition articulated by Henson, Lal and Pusey (HLP). Considering all scenarios with up to 4 observed variables, which number in the thousands, we are able to resolve all but three causal scenarios, providing evidence that the HLP condition is, in fact, exhaustive.

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